Analysis of a long-lived, two-cell lightning storm on Saturn

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Analysis of a long-lived, two-cell lightning storm on Saturn

G. Fischer, J. Pagaran, P. Zarka, M. Delcroix, U. Dyudina, W. Kurth, D.

Gurnett

To cite this version:

G. Fischer, J. Pagaran, P. Zarka, M. Delcroix, U. Dyudina, et al.. Analysis of a long-lived, two-cell lightning storm on Saturn. Astronomy and Astrophysics - A&A, EDP Sciences, 2019, 621, pp.A113.

�10.1051/0004-6361/201833014�. �hal-02178180�

Analysis of a long-lived, two-cell lightning storm on Saturn ^?

G. Fischer

, J. A. Pagaran

, P. Zarka

, M. Delcroix

, U. A. Dyudina

, W. S. Kurth

, and D. A. Gurnett

1Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria e-mail:georg.fischer@oeaw.ac.at

2 Institute of Physics, University of Graz, Universitätsplatz 5, 8010 Graz, Austria

3LESIA, Observatoire de Paris, CNRS, PSL, UPMC/SU, UPD, 5 Place Jules Janssen, 92195 Meudon, France

4Commission des observations planétaires, Société Astronomique de France, Paris, France

5Geological and Planetary Sciences, 150–21, California Institute of Technology, Pasadena, CA 91125, USA

6Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242, USA

ABSTRACT

Lightning storms in Saturn’s atmosphere can last for a few days up to several months. In this paper we analyze a lightning storm that raged for seven and a half months at a planetocentric latitude of 35^◦south from the end of November 2007 until mid-July 2008. Thun- derstorms observed by theCassinispacecraft before this time were characterized by a single convective storm region of∼2000 km in size, but this storm developed two distinct convective storm cells at the same latitude separated by∼25^◦in longitude. The second storm cell developed in March 2008, and the entire two-cell convective system was moving with a westward drift velocity of about 0.35 deg per day, which differs from the zonal wind speed. An exhaustive data analysis shows that the storm system produced∼277000 light- ning events termed Saturn electrostatic discharges (SEDs) that were detected byCassini’s Radio and Plasma Wave Science (RPWS) instrument, and they occurred in 439 storm episodes. We analyzed the SED intensity distributions, the SED polarization, the burst rates, and the burst and episode durations.

During this stormCassinimade several orbits around Saturn and observed the SEDs from all local times. A comparison with optical observations shows that SEDs can be detected when the storm is still beyond the visible horizon. We qualitatively describe this so- called over-the-horizon effect which is thought to be due to a temporary trapping of SED radio waves below Saturn’s ionosphere. We also describe the first occurrence of so-called SED pre- and post-episodes, which occur in a limited frequency range around 4 MHz separated from the main episode. Pre- and post-episodes were mostly observed byCassinilocated at local noon, and should be a manifestation of an extreme over-the-horizon effect. Combined radio and imaging observations suggest that some decreases in SED activity are caused by splitting of the thunderstorm into a bright cloud and a dark oval.

Key words. planets and satellites: atmospheres – planets and satellites: gaseous planets – methods: data analysis

1. Introduction

Radio emissions from Saturn lightning were detected by both Voyagers (Warwick et al. 1981,1982) and by theCassinispace- craft (Fischer et al. 2006), and the strong intensities of Sat- urn lightning also led to a detection with radio telescopes on Earth (Zakharenko et al. 2012; Konovalenko et al. 2013). The Saturn electrostatic discharges (SEDs) are typically 10 000 times stronger than terrestrial “sferics” (short for radio signals from atmospheric lightning) in the frequency range of a few MHz (Fischer et al. 2006). They were found to be related to con- vective clouds that can easily be observed with the Cassini camera as well as with ground-based optical telescopes of ama- teur astronomers (Porco et al. 2005;Dyudina et al. 2007;Fischer et al. 2007a;2007b;2011a;2011b;Sánchez-Lavega et al. 2011).

Thunderstorms in Saturn’s atmosphere are formed by strong vertical convection or updrafts that lead to visible white plumes consisting of high-altitude clouds (Hueso & Sánchez-Lavega 2004; Fischer et al. 2008;Read 2011). These clouds overshoot the outermost ammonia cloud layer, from where they are observ- able by a space-borne satellite such asCassinior ground-based amateur astronomers. Saturn lightning flashes were optically

?Table C.1 is only available at the CDS via anony- mous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/621/A113

observed for the first time around Saturn equinox in 2009 when the ring shine was minimal allowing the detection of illumi- nated cloud tops on Saturn’s night side by theCassini camera (Dyudina et al. 2010). From these observations the flash depth was restricted to 125–250 km below the upper cloud layer. The most likely location of Saturn lightning flashes is within its water cloud layer. The main charges in terrestrial thunderclouds are created in a temperature range from −10 to −25^◦C (Rakov &

Uman 2003), and such temperatures can be found in Saturn’s water cloud layer at pressure levels of 8–10 bar, roughly 200 km below the cloud tops (Fischer et al. 2008). Hence, a similar charging process is likely at work on Earth and on Saturn.

Until the occurrence of the “Great White Spot” (Fischer et al.

2011b), a region called the “storm alley” at the planetocentric latitude of 35^◦ south was the most active region on the planet in theCassiniera (Fischer et al. 2011a). Convective outbursts of irregular shape (typically circular or oval) with active temporal evolution and a size of∼2000 km were growing there and decay- ing in a matter of days, weeks, or even months. The Great White Spots (GWS) as biggest convective outbursts on Saturn can have latitudinal extensions of 10 000 km (Sanchez-Lavega & Battaner 1987), and they typically occur about once per Saturn year (29.5 Earth years). The last GWS developed at 35^◦N in December 2010, and it developed an eastward tail that wrapped around the whole planet within a few weeks (Fischer et al. 2011b;

Sánchez-Lavega et al. 2011). Thanks to Cassini and ground- based observations the atmospheric dynamics of the last GWS was well characterized (e.g., Sayanagi et al. 2013, Sánchez-Lavega et al. 2019).García-Melendo et al. (2013) pre- sented winds in the storm from Cassini observations and the vertical cloud structure from radiative transfer and dynamical modeling. Lightning activity in the GWS lasted until August 2011 with peak rates around 10 SEDs per second. This is about one to two orders of magnitude larger than the rate in the smaller

∼2000 km sized thunderstorms, where it is typically a few SEDs per minute. Such smaller convective outbursts are much more common. They occurred at a planetocentric latitude of 35^◦N in the Voyager era (Hunt et al. 1982; Sromovsky et al. 1983;

Ingersoll et al. 1984) and at 35^◦S in theCassiniera (Porco et al.

2005;Vasavada et al. 2006;Fischer et al. 2007b;Dyudina et al.

2007). The Voyager SED storms occurred shortly after vernal equinox (Saturn solar longitude LS from 2^◦ to 12^◦), and the Cassiniera SED storms in the storm alley at 35^◦S were observed in the time interval from May 2004 until July 2010, that is from shortly after southern summer until vernal equinox (LS from 284^◦to 5^◦).

In this paper we return to the smaller, 2000 km convective- type thunderstorms on Saturn and analyze in detail an SED storm that lasted from 27 November 2007 until 15 July 2008.

This storm is called SED storm F, following previous storms dubbed storm 0 and storms A–E (Porco et al. 2005; Fischer et al. 2007a; Dyudina et al. 2007). Storm F was not the last 2000 km sized storm, but there were a few more in the southern hemisphere before the GWS and a few afterwards in the northern hemisphere.

In Sect. 2, the trajectory of Cassini during SED storm F will be shown, and we will briefly describe theCassiniRPWS (Radio and Plasma Wave Science) instrument and the optical instruments used for this study. Together with an overview of the SED activity, images of the storm taken by theCassinicamera and the longitudinal drift of the storm derived from ground- based telescopic observations andCassiniwill be presented in Sect. 3. In Sect. 4 a statistical analysis comprising the physi- cal characteristics of SED intensities, polarization, burst rates, and episode durations will be presented. The paper continues with Sect.5, where we will discuss SED pre- and post-episodes, the distribution of episodes in subspacecraft western longitude, the over-the-horizon effect, the continuous SED detections of 6–10 March 2008, the occurrence of dark ovals, and the splitting of a convective system. A summary with conclusions (Sect.6) ends this paper. An appendix is provided to describe theCassini RPWS observational modes and polarization measurements, and a list with the main physical characteristics of all 439 SED episodes is provided as supplementary material.

2. Observational geometry and instruments 2.1. Observational geometry

Figure 1 shows a three-dimensional view of the Cassini tra- jectory from the start to the end of SED storm F. During this time SEDs were observed for the first time from all local times (LT) since previous storms had only been observed from Saturn’s morning side (Fischer et al. 2006;2007b).

The SED storm started on day of year (DOY) 331 of 2007 (27 November) and ended on DOY 197 of 2008 (15 July);

these times are marked in the figure by a triangle and a square, respectively. During those 232 days theCassinispacecraft made 25 orbits of varying apoapse and periapse distances around

0

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−5 0 5 10 15

y [R_S] Cassini trajectory (equatorial system)

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Fig. 1. Illustration of Cassini’s trajectory (about 25 orbits) during the SED storm from 27 November 2007 (marked by a triangle) until 15 July 2008 (marked by a square) in Saturn’s equatorial system. The trajectory is colored from blue (low inclination orbits) to red (high incli- nation orbits) to follow its temporal evolution. Saturn is schematically illustrated at the origin of the coordinate system with thez-axis along Saturn’s rotation axis, and the positivex-axis points toward the Sun in a plane formed by the rotation axis and the line from Saturn to the Sun.

Saturn with orbital periods declining in steps from 16 to 7 days. The periapse passes took place on the night side around midnight, and the apoapse passes shifted from early afternoon to shortly before noon. Cassini was mostly on the morning side in the southern hemisphere, and on the afternoon side in the northern hemisphere. The orbital inclination of Cassini increased from∼12^◦in kronocentric latitude to∼75^◦in latitude with time by Titan gravity-assisted maneuvers. To raise the orbital inclination, Titan flybys T38 to T44 were made at the outbound leg around a Saturn local time (LT) of 11 h, and Cassini’s various orbital periods (∼16, 12, 10.6, 9.6, 8.0, and 7.1 days) had different resonances with Titan’s orbital period of 16 days. The apoapse distance decreased in steps from∼37RS

(Saturn radii, 1RS= 60,268 km) to 21RS during the course of SED storm F (see Fig.1).

2.2. Cassini RPWS

The radio bursts of Saturn lightning were observed with the Cassini Radio and Plasma Wave Science (RPWS) instrument (Gurnett et al. 2004). In the frequency range of the SEDs the RPWS High Frequency Receiver (HFR) acted as a frequency sweeping receiver and swept from 325 kHz to∼16 MHz with an instantaneous bandwidth of 25 kHz within a few seconds.

Different frequency step sizes, integration times, and antennas could be chosen resulting in many different observational modes.

However, there were three prevalent modes with which the SEDs were observed (Fischer et al. 2011c), namely: (i) the survey mode, (ii) a fast polarimeter survey mode, and (iii) the so-called direction-finding (DF) mode (Cecconi & Zarka 2005). These modes are characterized by different duty cycles and detection efficiencies with respect to SEDs (see Appendix A). Shorter sweeping intervals and the usage of the more sensitive dipole in the survey mode typically led to about four to five times more SEDs in the survey mode (i) compared to the DF-mode (iii), where, in the latter mode, the RPWS monopole antennas are used. A description of how SEDs are extracted from RPWS data

330 340 350 360 001 010 020 030 040 050 060 070 10⁰

10¹ 10² 10³ 10⁴

DOY 2007/2008

Detected SEDs per hour

Dec 1 Dec 15 Jan 1 Jan 15 Feb 1 Feb 15 Mar 1

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Time (year 2007/2008) Cassini distance [R S]

Fig. 2. Number of detected SEDs per hour in logarithmic scale as a function of time (in DOY 2007/2008,upper panel), and radial distance of Cassinias function of time (lower panel). This figure gives the first part of SED storm F from late November 2007 until 9/10 March 2008. The periapse times are marked by dotted vertical lines in both panels. The horizontal lines at the top indicate times when SED episodes lasted for a full Saturn rotation.

and the prescribed intensity thresholds are given inFischer et al.

(2006) and in AppendixBof this paper. Furthermore, the way SED polarization is measured is also described in more detail in this appendix.

2.3. Cassini ISS

The images shown in the next section were taken by the Wide Angle Camera (WAC) of theCassiniImaging Science Subsys- tem (ISS,Porco et al. 2004). The WAC is a wide-angle refractor with 0.2 m focal length and a field of view of 3.5^◦and a CCD detector consisting of a 1024 square array of pixels. The storm clouds can be imaged with many filters that provide estimates of the cloud altitudes, for example, the narrow-band (5–20 nm wide) filters at the methane absorption bands MT1, MT2, and MT3 can probe different altitudes in the atmosphere. MT1 (cen- tral wavelength at 619 nm) and MT2 (727 nm) sense lower and intermediate cloud altitudes, respectively. Storm clouds were even seen at the strong methane absorption band MT3 at 889 nm.

At this wavelength, MT3 senses the highest part of Saturn’s atmosphere, and the absorption optical depth of one (i.e.,τ=1) occurs at a pressure level of 0.33 bars (Dyudina et al. 2007).

During SED storm F the cloud features were imaged by the ISS camera on seven different days, namely 6 December 2007, 4 March, 23 April, 19 May, 4 June, 18 June 2008, and 10 July 2008.

The clouds were seen in day side images, typically observed with the clear filters (CL1, CL2) or the continuum band filters (CB1 at 619 nm, CB2 at 750 nm, CB3 at 938 nm).

2.4. Ground-based instrumentation

TheCassinioptical observations are complemented by ground- based observations made by amateur astronomers. The latter

provide more extended temporal coverage by monitoring the storm shape evolution and its longitudinal drift. The amateurs observed the storms on more than 70 days in the time inter- val from the beginning of December 2007 until the end of June 2008. The optical telescopes used by amateurs are mostly reflec- tors with an aperture from 15 to 40 cm (Delcroix & Fischer 2010). Many amateurs post their images at the website of the Planetary Virtual Observatory and Laboratory¹ (Hueso et al.

2010) or the Association of Lunar and Planetary Observers (ALPO) of Japan².

3. Observational records 3.1. Radio records

The SED storm before storm F had taken place in January and February 2006, and it was designated with the letter E (Fischer et al. 2007b). After storm E there was a long quiet period of about 21 months. During this time no SEDs and no prominent storm cloud features were observed by theCassiniinstruments (Fischer et al. 2008). SED storm F described in this paper started in November 2007. We divide SED storm F into two different time intervals (Fischer et al. 2011c). Figure2shows the first inter- val of SED storm F from late November 2007 until early March 2008. The second interval of SED storm F displayed in Fig.3 goes from early March 2008 until mid-July 2008. The first inter- val is characterized by a single storm cell. In the second interval SED storm F consists of two storm cells at the same latitude, but separated by∼25^◦in longitude.

1 http://www.pvol.ehu.es/

2 http://alpo-j.asahikawa-med.ac.jp/

070 080 090 100 110 120 130 140 150 160 170 180 190 200 10⁰

10¹ 10² 10³ 10⁴

DOY 2008

Detected SEDs per hour

Mar 15 Apr 1 Apr 15 May 1 May 15 Jun 1 Jun 15 Jul 1 Jul 15

0 10 20 30

Time (year 2008) Cassini distance [R S]

Fig. 3. Number of detected SEDs per hour as a function of time (in DOY 2008,upper panel), and distance ofCassinias function of time (lower panel). This figure gives the second part of SED storm F from 10 March until 15 July 2008. Similar to the previous figure, the periapse times are marked by dotted vertical lines in both panels, and the horizontal lines indicate times when SED episodes lasted for a full Saturn rotation.

The upper panels of Figs. 2 and 3 show the number of detected SEDs per hour as a function of time, and the lower panels show the spacecraft distance to Saturn. The vertical dot- ted lines in both panels of these figures indicate the times when theCassinispacecraft was at periapses. The number of detected SEDs not only reflects the strength of the thunderstorm, but it is also a function of many observational parameters. The most influential parameter is the distance of the spacecraft, since the SED intensity falls off with distance squared, and so many low intensity SEDs are below the background level at large distances.

Other observational parameters (see appendix) are the receiver mode, the attitude of the spacecraft, or the local time of the storm since the low-frequency cutoff of the SEDs is set by different peak electron densities in Saturn’s ionosphere on the day- and night side (Fischer et al. 2011c). From the vertical dotted lines in both panels of Figs.2 and3 one can see that peaks in SED numbers are mostly found around periapse passes.

Viewed from Cassini, SEDs from a single storm usually occur in episodes which start (stop) at the time when the storm enters (exits) the radio horizon. In general, the radio horizon of SEDs is not identical to the visible horizon of the storm seen from Cassini. It has been shown with previous SED storms, that the radio horizon usually extends beyond the visible hori- zon, which is called over-the-horizon (OTH) effect (Zarka et al.

2006;Fischer et al. 2007b). SED episodes are usually separated from one another by a quiet period of a few hours (absence of SED detections), since the presumably active storm on the other side of the planet (beyond the radio horizon) cannot be observed.

In case of two storm cells with ∼25^◦ longitudinal separation (second part of SED storm F) the episodic on–off behavior is practically unchanged, only the SED activity will occur over an increased longitude range. In Figs. 2 and 3 the episodic

behavior can hardly be seen due to the highly compressed time scale and the limited resolution of the figure (see e.g., Fig. 2 of Fischer et al. 2007bto discern episodic behavior). There are a few instances of time when the SEDs can be detected for more than a full Saturn rotation with no quiet period between consecu- tive episodes. Those times are marked with thick horizontal lines at the top of the upper panels in Figs.2and3. One can see such lines three times after periapse passes in Fig. 2, and 14 times after periapse passes in Fig.3. We believe that this is due to the over-the-horizon effect combined with a better visibility of the southern storm from higher southern spacecraft latitudes dur- ing periapse passes (see Sect.5.3). However, in Fig.2 there is one instance with continuous SED detections taking place when Cassiniis more distant and located in the northern hemisphere.

This is the case from 6–10 March when the RPWS instrument recorded no episodic gaps for nine consecutive Saturn rotations.

This can only be explained by the presence of another storm, and we will discuss the reasons for the continuous SED detection in more detail in Sect.5.4.

Figure2shows that the first part of storm F has several gaps in SED activity lasting for a few days or several Saturn rota- tions. For example, there is almost no SED activity for nearly five days right after periapsis of 27 January 2008. These gaps are due to internal variations of the strength of the thunder- storm, and such strong variations have been observed in previous storms (Fischer et al. 2006). We propose that some declines in SED activity during SED storm F are related to a splitting pro- cess of convective thunderstorm cells. This will be discussed in more detail in Sect.5.6. Figure3shows the second part of SED storm F from early March until mid-July, where there are fewer gaps in SED activity. For example, there is one gap in SED activ- ity from 11 to 14 March. There is strong evidence that there was

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Western longitude [°]

Time [Year 2007/2008]

F¹

F² S³

Storm F¹ Storm F² Spot S³ other

south. For example, one can easily identify 3 dark spots between the two white spots in the Fig. 4. Location of cloud features as a function of time as imaged by Cassini(diamonds) and ground-based amateur astronomers (dots). All longitudes in this figure and paper are western longitudes in degrees of Voyager SLS. Thex-axis was inverted to have larger western longitudes on the left side. They-axis goes from the start of storm F (27 November 2007) until its end (15 July 2008) with the start of the storm on the top. The different colors denote the storm cellsF¹,F² and spotS³ as discussed in the text.

a second active storm cell during the second part of the storm displayed in Fig.3. This might be the reason for fewer gaps in SED activity, since it is less probable that two storm cells are inactive at the same time compared to just one inactive storm cell.

3.2. Images

Storm systems with SED activity appear as bright white spots, most likely due to overshooting cloud tops as a result of a sudden increase in cloud vertical growth from updraft intensification.

They are usually easy to identify on images of Saturn taken by the Cassinicamera as well as on high quality images from ground-based telescopes made by amateurs (Porco et al. 2005;

Delcroix & Fischer 2010). The prominent cloud features related to SED storm F were observed both by space- and ground-based instruments. The Cassinicameras imaged the clouds on seven different days mentioned in Sect.2.3, and ground-based images show storm clouds starting from 1 December 2007 until 30 June 2008. The optical images showed that there is not only a single predominant cloud feature like in previous storms, but after mid- March 2008 there are at least two longitudinally separated storm cells.

Figure4shows the longitudinal location of prominent cloud features around 35^◦S planetocentric latitude from ground-based observations andCassiniISS images as a function of time. The main cloud feature was centered around 36^◦S planetocentric lat- itude from the beginning to the end of the storm, and it drifted from∼270^◦ to almost∼350^◦western longitude. All longitudes (and drift rates) in this paper are given in Voyager SLS (Desch &

Kaiser 1981). The main featureF¹is marked as red line in Fig.4, and a linear fit of all red points (from ground-based amateur as well asCassinimeasurements) gives a drift of (0.35±0.01)^◦per Earth day. Taking the most prominent features from theCassini ISS images from 6 December 2007 (DOY 340, at 275^◦) and 4 March 2008 (DOY 64, at 302^◦) the drift is slightly smaller with 0.30^◦ per day which is the value given by Fischer et al.

(2011c) for the first part of SED storm F. We also note that the

longitudinal as well as latitudinal extension of the storm is typically about 2^◦−3^◦.

In mid-March 2008, a second bright cloud spot appeared around 38^◦S planetocentric latitude and around 280^◦longitude, roughly∼25^◦further east from the main drift lineF¹. This sec- ond storm marked with the green drift line F² was observed by many amateurs and Cassini, and it drifted at a rate of (0.35±0.02)^◦ per day. So due to the similar drift of cloud fea- tures F¹ andF² the longitudinal distance between both storm clouds was almost constant. Interestingly, this second storm cell F²occurred in mid-March 2008 at a longitude around 280^◦, only 10^◦ westward from where the first storm cell F¹ emerged in late November 2007. The emergence of the second storm cell could be due to instabilities created by the first storm at the same longitude, or due to gravity waves from the first storm which have been observed to create additional cells in terrestrial thunderstorms (Balachandran 1980). This is similar to the later Great White Spot on Saturn, where additional thunderstorm cells developed in its eastward tail (Sayanagi et al. 2013).

Figure4also shows the drift of a third cloud feature called S³. This third cloud feature at 35^◦S planetocentric latitude existed from the end of January 2008 until the beginning of April 2008. Compared toF¹andF², cloud featureS³had a faster drift of (0.92±0.02)^◦ per day (blue line in Fig. 4). In the ground- based imagesS³rather appeared as a faint spot in contrast toF¹ andF²which both appeared as bright white spots. We will dis- cuss in Sect.5.3that the featureS³probably did not show any SED activity, which is why we call it “spot” and not “storm”.

The red, green and blue lines in Fig.4describe the drifts of the cloudsF¹,F² andS³, respectively. The linear dependence of their western longitudesθ_i (in degrees of Voyager SLS) as a function of timedi(DOY 2007) is as follows:

F¹: θ₁=0.346d₁+154.87 with 331≤d₁≤562, (1) F²: θ₂=0.354d2+123.88 with 439≤d2≤535, (2) S³: θ₃=0.924d3−71.63 with 392≤d3 ≤460. (3) StormF¹ lasted from 27 November 2007 until 15 July 2008. It was imaged for the first time on 1 December 2007 and for the last time on 30 June 2008, but in this case we set the limits from the beginning until the end of the SED activity. StormF² was observed optically from 14 March until 18 June 2008, although its SED activity probably last several days longer. The cloud fea- tureS³lasted from 27 January to 4 April 2008, as indicated by the limits fordiin DOY 2007 in the equations above.

The drift of the storm cells around 0.35^◦per day corresponds to a westward wind speed of about 3.3 m s⁻¹with respect to the Voyager SLS rotation period. This is similar to previous SED storms of 2004–2006 around 35^◦S latitude, whose drift rates were in the range from 0.2–0.6^◦ per day (Dyudina et al. 2007), corresponding to wind speeds of∼2–6 m/s. It is interesting to note that the zonal wind speed profile measured byCassiniISS shows a westward peak velocity of (11.4±3) m/s at that lati- tudes (García-Melendo et al. 2011). This difference could partly be due to vertical wind shear, which is a prerequisite for storm splitting as discussed in Sect.5.6. Additionally, the peak of the westward jet is located at 34^◦S, whereas the storm cells rather tend to be centered around 36^◦S (Vasavada et al. 2006;Dyudina et al. 2007;Del Genio et al. 2007; Sromovsky et al. 2018), so there could be a small latitude difference. The drift speed of spotS³ with 0.92^◦ per day corresponds to a speed of 8.9 m/s, which is within the error bars of the environmental wind given by García-Melendo et al.(2011). The drift speed of the head of the

Fig. 5. Amateur images of Saturn with south pointing upward from February and March 2008.Left panel: RGB image of Saturn taken by Jean- Jacques Poupeau on 23 February 2008, 23:47 UT. The prominent cloud feature close to the central meridian is the storm cellF¹. The faint cloud feature about 20^◦westward ofF¹ is marked with red lines, and this is spotS³as discussed in the text.Right panel: Saturn image in green filter taken by Maximo Suarez on 6 March 2008, 23:20 UT. The magnifiedinset panelshows four features named A, B, C, and D, where the latter is questionable. Feature A corresponds to storm cellF¹with feature B being a westward extension of A. Feature C corresponds to spotS³.

Fig. 6. CassiniISS images from 4 March 2008 (left panel), and 18 June 2008 (right panel). The left image shows mainly one bright storm cloud, whereas there are two bright storms in the right image. In the 4 March image the bright stormF¹ is located at 302^◦ western longitude. We have marked the features A, B, and C corresponding to the features shown in the right panel of Fig.5, that were imaged by M. Suarez two days later.

This shows that spotS³is actually a large dark oval. The 18 June image shows two bright spots at 310.3^◦(F²) and at 343.4^◦(F¹) western longitude, with the older storm cellF¹further west (left) than the younger storm cellF². All spots are located around∼35^◦south planetocentric latitude. The left image (file name W00043078.jpg) was taken with filters CB3 and CL2, and the right image (file name W00046585.jpg) was taken with filters CB3 and IRP0 (Images by NASA/JPL/SSI).

Great White Spot was even further away from the environmental winds: its westward drift rate of 2.8^◦ per day corresponds to a wind speed of about 27 m/s (Sayanagi et al. 2013), and storms drifting with a different velocity than the environmental winds are suggestive of deeply rooted convection at the water cloud level (Sánchez-Lavega et al. 2011).

The amateur images of Saturn from February and March 2008 not only show the single storm cellF¹, but there is also another cloud feature named spot S³ which is thought to have

no SED activity. Figure5 illustrates this with two images, one from 23 February and another one from 6 March. The latter even shows an extended storm cellF¹, and it is interesting to compare it with theCassini ISS image taken two days earlier. Figure6 shows twoCassiniimages from 2008 with the storm clouds. The left image taken on 4 March shows the single bright stormF¹, and we have also indicated the features A, B, and C correspond- ing to the right image from Fig. 5. The largest cloud feature A corresponds to the storm cloudF¹.The leftCassiniimage of

Fig.6actually shows that features B and C are dark ovals. Fea- ture B, which looks like a westward extension of A (F¹) in the ground-based image, turns out to be a dark oval being close to stormF¹. Feature C corresponding to spotS³also turns out to be a large dark oval in the high-resolutionCassiniimage. The differ- ent appearance is mostly due to the usage of different filters in the ground-based image (green filter) versus theCassiniimage (con- tinuum band filter CB3 around 938 nm). There is also aCassini image from 4 March taken with a green filter (not shown), which shows faint white spots as features B and C. Furthermore, some dark vortices are sometimes accompanied by bright features as well. The notion that spot S³ is actually a large dark oval is also supported by an image taken with CassiniVIMS (Visual and Infrared Mapping Spectrometer) on 9 February 2008.

Figure 5 inSromovsky et al.(2018) shows this dark oval around 300^◦western longitude (60^◦eastern longitude), about 8^◦in lon- gitude westward of the bright thunderstorm. These longitudes are consistent with the longitudes ofS³andF¹ shown in Fig.4for the first half of February 2008. The reason why only this dark oval (and not numerous other ones) was seen as faint spot in the ground-based images is probably its exceptionally large size.

There are no otherCassiniISS images of spotS³except those of 4 March.

The right image taken on 18 June shows a pair of bright white features (F¹ on the left,F² on the right) at the same lat- itude, separated by about∼33^◦in longitude. For the observation of 18 June the observed storm cloud longitudes are somewhat off from the linear fits of Eqs. (1) and (2). Using the fitted lines the longitudinal difference between stormsF¹andF²varies only from∼26.7^◦to∼27.5^◦. Again one can see some more dark ovals which are located at the same latitude as the bright spots in the well-known storm alley at ∼35^◦ south. For example, one can easily identify 3 dark spots between the two white spots in the 18 June image of Fig.6(right panel). The relation between the dark ovals and the convective storms will be further discussed in Sect.5.5in comparison with previous works (Dyudina et al.

2007;Baines et al. 2009;Sromovsky et al. 2018). It is likely that the SED activity of storm cellF² started exactly on 14 March 2008, since this is the first day when we have a clear evidence of it in ground-based images³. Furthermore, there was very little SED activity from 10 March noon until 14 March at 06:00 SCET (see Fig. 3), and SED rates started to rise again exactly on 14 March. The exact end of SED activity in storm cellF²can not be determined since it is impossible to distinguish it from SEDs fromF¹.

4. Statistical analysis

In this section we analyze the SED intensities, polarization, burst rates, and the durations of the SED episodes for the complete storm. Using the detection criteria described in Fischer et al.

(2006) and in the appendix, 277 046 SEDs were detected dur- ing storm F. The SEDs were made up of more than half a million SED pixels (500 492 single time–frequency measurements). One SED is produced by a single lightning event. Since its duration can be longer than the receiver integration time (typically 35 ms) at one frequency, several measurements at successive frequency channels (“SED pixels”) can be made during one SED. Using the numbers above, an average SED consists of 1.8 SED pix- els. About 68.5% of the SED pixels were detected in the survey mode,∼23.0% in the fast polarimeter mode, and∼8.5% in the

3 Not shown here, see e.g., the image of Carmelo Zannelli on http://pvol2.ehu.eus/pvol2/.

10⁰ 10¹ 10²

0 10 20 30 40 50

Distance from storm F1 to Cassini [R

S]

Intensity above background [dB]

SED intensity as a function of distance Median (50%) 80%

95%

Max.(100%)

Fig. 7. Intensities of SED storm F pixels as a function of distance between storm F¹ andCassini. The data was divided in 18 distance intervals with a bin size of 2RS, centered at the values of 3, 5, 7, ...

37RS. For each interval we calculated the median intensity value (50%

percentile, blue curve), the 80% percentile (green curve), the 95% per- centile (red curve), and the maximum (100% percentile, cyan curve).

The gray line represents an inverse-square law (_r¹2) dependence.

DF-mode. The number of SEDs detected during SED storm F is a factor of about 12 higher than all SEDs detected by both Voyagers (∼23 000 SEDs), and a factor of 5–6 higher than all SEDs detected by Cassini during the previous shorter storms (∼49 000 SEDs). Hence, we employ a statistical analysis and compare the results with previous storms.

4.1. SED intensities

Since the geometrical dimensions of the SED source are much smaller than the distance to the observer, the SED intensity is an inverse-square function of distance. Using such an approach, Zarka(1985) obtained a reasonable agreement between model and measurements of the variation of SED maximum intensity as a function of time during the Voyager 1 flyby. PreviousCassini SED measurements with sufficient SED rates were made only during parts of one orbit with small variations in distance. For storm F the distance variation was more than one order of mag- nitude (about 3RS to about 37RS). Figure7shows a statistical analysis of the SED intensities as a function of distance. We binned all SEDs as a function of their distance to the planet in 18 bins with a bin size of 2RS(centered at values from 3RS to 37RS). For each bin we calculated the intensities of the per- centiles of 100, 95, 80, and 50%. The 50% percentile is the median value, and half of the SED pixels in that bin are smaller than the median intensity. The intensities of the 100% percentile represents the maximum, and SEDs are detected from the detec- tion threshold (see appendix) up to the maximum intensity. The cyan curve as the maximum SED intensity in Fig.7follows the inverse-square law relatively well (gray line). The same holds for the red curve representing the 95% percentile. The small varia- tions in the curves are probably due to the internal variation of the storm’s intensity or due to different ionospheric conditions.

There are probably no beaming effects since SEDs are thought to radiate isotropically (Zarka 1985), but absorption generally depends on the ionospheric electron density which is varying with local time. The most intense SED pixel was detected on

18 May 2008 at 02:01 SCET (spacecraft event time) with an intensity of 39.5 dB above the background. The mean inten- sity of all storm F SED pixels is 6.0 dB, and the median intensity is 3.9 dB. After the model of Dulk et al. (2001) the galactic background has a relatively constant flux density of

∼10⁻¹⁹W m⁻²Hz⁻¹in the frequency range of the SEDs from 2 to 16 MHz (see Fig. 1 inZarka et al. 2004). This means that the flux densities of the detected SED pixels range over almost four orders of magnitude from∼10⁻¹⁹ to∼10⁻¹⁵ W m⁻² Hz⁻¹. The antenna resonance around 7–8 MHz is also in the SED frequency range, but it enhances both the background and the signal.

The distribution of SED intensities approximates an expo- nential law as can be seen in Fig. 8. Similar distributions for single SED episodes have already been shown inFischer et al.

(2007b). The small plateau in the first one or two bins close to the intensity threshold for the distribution of intensities over all episodes is due to the detection algorithm (see appendix) in com- bination with the varying distance of the spacecraft. In Fig.8 we also show the relative similarity of the intensity distribu- tion of all SED pixels (in gray) to those from the single episode (in black) of 10 May 2008 before noon, whenCassiniwas very close to Saturn. We also note that for such a closest approach episode, where SED intensities typically extend over more than three orders of magnitude (see Fig.7), the shape of the distribu- tion is similar to an exponential decay. Only the SEDs above the intensity threshold are detected, and these SEDs lie on the tail of a distribution whose shape can also be modeled with a general- ized extreme value distribution (Pagaran & Fischer 2014). With such a model fit it could be possible to roughly estimate the num- ber of SEDs below the detection threshold. Here we only use a two-term exponential model to fit the distribution of all SED intensities. The dashed fitted curve in Fig.8is given by

N=1.35×10⁴exp(−0.12I)+5.07×10⁴exp(−0.41I), (4) withIas the intensity in dB above background andNas the num- ber of SED pixels. The first term approximates the intensities above∼5 dB, whereas the second term mainly fits the intensities below∼5 dB. The first bin was not included in the fit due to the close threshold level.

4.2. SED polarization

The polarization of SED radio waves is an important prop- erty with which the hemisphere and the emission mode of the SED source can most likely be determined. The methodology to determine the SED polarization from RPWS measurements is described in Fischer et al. (2007a) and shortly summarized in AppendixBof this paper.Fischer et al.(2007a) found right- hand polarized SEDs below 2 MHz from a southern hemisphere source and suggested that the polarization sense is related to the direction of the magnetic field in the two hemispheres rel- ative to the radio wave propagation vector. They suggested that the ordinary mode is dominant (the extraordinary mode is more attenuated) leading to right-handed SED polarization from southern hemisphere sources since the radio wave propagation vector is opposite to the magnetic field vector there. Conse- quently, SEDs from the northern hemisphere should be left-hand polarized, which was the case for the SEDs from the first giant thunderstorm of 2010/2011 observed in the northern hemisphere byCassini(Fischer et al. 2011b).Fischer et al.(2007a) measured the SED polarization of SED storm E from January and February 2006, and since then several other SED storms have occurred at a latitude of 35^◦in the southern hemisphere, whose polarization analyses are yet to be performed.

0 5 10 15

0 1 2 3 4 5 6 7 x 10⁴

Intensity above background [dB]

Number of SED pixels

Distribution of intensities all episodes one episode (x10) fitted curve

Fig. 8. Distribution of SED pixel intensities of storm F with a bin size of 0.4 dB. The gray bars represent all SED pixels, and the black bars show the distribution of pixels from a single SED episode, the closest approach episode of 10 May 2008 before noon. For a better visibility the black bars of the single episode are magnified by a factor of 10 with respect to the scale on the ordinate. The dashed fitted curve is given by the two-term exponential model of Eq. (4).

The vast majority of SEDs from storm F below 2 MHz exhibit a right-handed circular polarization similar to storm E.

The polarization is described by the Stokes parametersq,u, and v. The median circular polarization of more than 6000 SED pix- els below 2 MHz from storm F isdc=v=−0.66, the median linear polarization isd_l= p

q²+u²=0.29, and the median total polarization isd= p

q²+u²+v²=0.77. Left-handed polariza- tion was found for only∼2.6% of the SED pixels. In principle, no SED should have a total polarization ofd>1, but about 5.1% of the SED pixels show a total polarization larger than one. This is mostly due to errors in the polarization measurement, which are typically around 15%. This confirms the results and conclusions ofFischer et al.(2007a).

We note that we also tried to perform a direction-finding analysis of storm F SED radio waves, since RPWS has such a capability, and since it would be interesting to see if in this way the two storm cells F¹ and F² could be discerned. However, this attempt was not successful. We used almost the same data as for the polarization measurements (i.e., below 2 MHz, see appendix), but limited them to aCassinidistance of less than 12 Saturn radii. From these∼5500 SED pixels, about 60% were retrieved in a 2-antenna mode, and about 40% with the 3-antenna mode. For the 2-antenna mode the direction-finding has to be done with the assumption of pure circular polarization (Stokes parametersq=0 andu=0), and this is a crude assumption since the median linear polarization of SEDs was found to bedl=0.29 (see above). As a consequence only 12% of the 2-antenna SED pixels had an incoming radio wave vector that originated from the planet Saturn. Surprisingly, this rate was even smaller (only 1.5%) for the the 3-antenna SED pixels for which no assumption about the linear polarization has to be made. The reason for this failure is most likely due to the fact that the RPWS 3-antenna direction-finding mode uses two consecutive 2-antenna mea- surements separated by 10–160 ms in time depending on the receiver mode (Gurnett et al. 2004, Vogl et al. 2004). Since SEDs are short and bursty signals, their properties might change

within this delay time of several tens of milliseconds, thereby corrupting the 3-antenna direction-finding measurement.

4.3. SED burst rates and durations

The SED burst rates highly depend on the distance of the space- craft to Saturn and are typically∼10² h⁻¹ at average distances and reach∼10³ h⁻¹at periapse as can be seen in Figs.2and3.

The highest rate of 3872 h⁻¹(about 1 SED per second) was mea- sured on 20 February 2008 from 13:00 to 14:00 SCET. With 277 046 SED detections (not SED pixels) during 2578 h one arrives at an average rate of 107 h⁻¹ (∼1.8 SEDs min⁻¹). The 2578 h is the sum of all episode durations during the 231.38 days (5553 h) of SED storm F from 27 November 2007 until 15 July 2008, that is SEDs were detected for slightly less than half of this time only when the storm was on the side of Saturn facing Cassini.

All the burst rates given so far are as detected, which means they do not account for the duty cycle of the instrument. The duty cycle gives the percentage of time the receiver dwells at SED fre- quencies, which depends on the mode of the instrument. For the mostly used survey mode the duty cycle is 32%, and a combined duty cycle taking into account the number of detected SEDs in each receiver mode is 34.4% (see appendix). The detected aver- age rate of 107 h⁻¹then corresponds to a so-called extrapolated or “true” rate of∼311 h⁻¹(∼5.2 SEDs min⁻¹) for SED storm F.

This rate is similar to the true rate of 367 h⁻¹of SED storm E (Fischer et al. 2007b). The SED peak detection rate of 3872 h⁻¹ during SED storm F was measured in the fast polarimeter mode with a duty cycle of 47% (see appendix), hence, the true peak rate would be 8238 h⁻¹ (or ∼2.3 SEDs per second). However, we note that these extrapolated values do not reflect the abso- lute SED rate of the storm. An increasing number of SEDs drops below the galactic background level for an increasing spacecraft distance, and we only see the tail of the intensity distribution (see Sect.4.1). Other factors influencing the SED detectability are the spacecraft-antenna attitude, the different sensitivities of RPWS dipole and monopole, and the local time of the source influenc- ing the SED ionospheric absorption and cutoff frequency. In a future paper we will try to get a better estimate for the true SED rate by taking all these points into account.

The SED burst durations follow an exponential distribution given byn ∝exp(−t/t0). This means that the number of SEDs n is exponentially decreasing with increasing burst duration t.

The distribution is characterized by the so-called e-folding time t₀with typical values from∼35 to∼50 ms (Fischer et al. 2008).

For example, the SEDs from the previous SED storm E recorded in the survey mode had an e-folding time of (49±3) ms (Fischer et al. 2007b). For SED storm F we found an e-folding time of (49±1) ms for the SED recorded in the survey mode (above 1825 kHz), and an e-folding time of (46±1) ms for the SEDs in the fast survey mode. The mean SED duration is (66±45) ms for the SEDs above 1825 kHz in the survey mode, and it is (54± 42) ms for the SEDs in the fast survey mode. The combined value for the mean SED duration in these two modes would be (63± 45) ms. The SEDs measured in the direction-finding mode (and in the survey mode below 1825 kHz) have such long integration times (>80 ms) that they would skew the result toward longer times, and so we excluded them here.

4.4. SED episode durations

SEDs are usually organized in episodes, lasting typically half a Saturn rotation. Saturn’s atmospheric storm features have a

0 2 4 6 8 10 12 14

0 5 10 15 20 25 30 35 40

Episode duration [h]

Numbers

pre+post−episodes regular episodes

Fig. 9. Distribution of SED storm F episode durations in half hour bins in a stacked histogram. The distribution contains 522 values, which includes 439 regular episodes, 49 pre-episodes, and 34 post-episodes.

higher angular velocity than the observerCassiniaround Saturn leading to a cessation of SEDs when the source is beyond the radio horizon. Figure9shows the distribution of episode dura- tions of all 439 SED storm F episodes plus so-called pre- and post-episodes that will be explained in the next subsection.

The duration of an SED episode depends on several fac- tors. Many SED episodes typically last somewhat longer than half a Saturn rotation (due to the over-the-horizon effect), and in Fig. 9 one can see a peak around an episode duration of six hours. This is followed by a sharp decline toward longer episode durations up to ten hours. The longer durations should be due to the addition of the second storm cell after March 2008 (see Figs.4and6) and an extension of the radio horizon when Cassini is at middle to high southern latitudes. There is even a small hump with episode durations from 10 to 13.5 h with some of these lasting even longer than the Saturn system III period of 10.6567 h (Desch & Kaiser 1981). These are the closest approach (periapsis) episodes whereCassinihas a high angular velocity (in the same sense as the rotation of Saturn) and can fol- low the SED storms for some time. This effect has already been modeled byZarka(1985) for the Voyager flybys of Saturn dur- ing which the SEDs were discovered. At large radial distances from Saturn a spacecraft can be regarded as an almost station- ary observer where the subspacecraft western longitude changes by 360^◦/10.66 h≈34^◦h⁻¹. During periapse passes with closest approach radial distances around 4RSthis rate went down below 20^◦h⁻¹ forCassini, thereby prolonging the time of visibility of an atmospheric feature. In the cases where one SED episode fol- lows immediately after the other (i.e., continuous SED detections without gap between episodes) it is sometimes difficult to tell when one episode ends and the next one begins. One way to do this is to place the boundary at the minimum of the SED rate pro- file. This was difficult during the interval 6–10 March 2008 when the SED activity and detection continued for nine consecutive Saturn rotations without interruption. In that case we arbitrarily placed the boundary between episodes at roughly the same sub- spacecraft western longitudes. We define one SED episode as the SED activity related to one Saturn rotation as viewed from the spacecraft. This means that we understand one Saturn rotation as the somewhat variable time (longer at periapsis!) during which the subspacecraft longitude completes 360^◦. So the continuous

13 14 15 16 17 18 19 20 21 22 2000

4000 6000 8000 10000 12000 14000 16000

Time [hr]

Frequency [kHz]

Episode F298 with pre−episode on 2008 DOY 127 from 13 to 22 SCET

pre−episode

main episode

<1.2 dB [1.2 1.6] dB [1.6 3.0] dB

>=3.0 dB

11 12 13 14 15 16 17 18

Time [hr]

Episode F036 with post−episode on 2007 DOY 352 from 11 to 18 SCET

post−episode main episode

<1.2 dB [1.2 1.6] dB [1.6 3.0] dB

>=3.0 dB

Fig. 10. Sample episodes with pre- and post-episodes.Left panel: storm episode F298 with a pre-episode.Right panel: episode F036 with a post-episode. We show the extracted SEDs displayed versus time (in hours of SCET, spacecraft event time) and frequency. The frequency range (with linear scale from 1.8 to 16.2 MHz) in the left and right panels are exactly the same. In the left panel nine hours are displayed, and in the right panel it is seven hours. The colors indicate the SED pixel intensities in dB above background.

SED detection from 6–10 March 2008 (DOY 066–070) consists of nine SED episodes (cf. episodes F175–F183 of Table C.1 in the supplementary material) and not just a single one. In Figs.2 and3 we have indicated the times when SED episodes lasted longer than one Saturn rotation which, with the exception of 6–10 March 2008, always happened at the periapse passes. The episodes from those times make up the small hump from 10 to 13.5 h in Fig.9.

The mean duration of the 439 regular episodes is 5.63 h. The longest SED episode lasted 13.36 h, and that was the periapsis episode of 16 June 2008 centered around noon (cf. episode F382 of Table C.1 available at CDS). This table enlists the most impor- tant characteristics of the 439 SED episodes. The table gives the episode name, center, start and stop times of each episode, the number of detected SEDs and SED pixels, the mean distance of Cassini, the subspacecraft western longitude at the episode cen- ter, and the subspacecraft western longitude range of the episode from the beginning to its end. The table also shows the 83 pre- and post-episodes. Pre-episodes are indicated by an additional letter “a” at the episode’s name, and for post-episodes the addi- tional letter “b” is used. Figure9 shows episode durations that are shorter than half a Saturn rotation. Some episodes are sim- ply shorter due to low SED rates. But, the peak in the first bins is due to the existence of what we call pre- and post-episodes. Their characteristics are described in more detail in the next section.

5. Discussion

This discussion section contains descriptions and investigations of noteworthy phenomena that occurred during SED storm F.

In the first subsection the new phenomenon of SED pre- and post-episodes is described. In the next subsection the course of the SED storm F is illustrated with a plot of the subspacecraft western longitude ranges of SED episodes as a function of time.

Here we will discuss if the second and third cloud features F² andS³ showed electrical activity or not. This is followed by a discussion of the over-the-horizon effect in the third subsection.

Next we will try to explain the continuous SED detection from 6–10 March 2008. In the fifth subsection we discuss the presence of dark ovals that are most likely not electrically active but are

seen in images throughout the lifetime of SED storm F. In the sixth and final subsection we consider the dynamics of Saturn’s thunderstorm and suggest that some decreases of SED activity might be related to splitting thunderstorm cells.

5.1. Description of SED pre- and post-episodes

Figure10shows a typical pre-episode in the left panel, and a typ- ical post-episode in the right panel, displayed as extracted SEDs versus time and frequency. The left panel shows a pre-episode with a duration of about two hours (from 14 to 16 h SCET), which is separated by at least one hour from the main episode, which starts after 17 h SCET. Its most striking characteristic is its limited frequency range from∼2−6 MHz. Similarly, the right panel shows a so-called post-episode around 17 h SCET, which appears to be separated from the main episode and starts roughly one hour after the main episode ended. Its frequency range is even more limited, from ∼2−4 MHz. In summary, the limited frequency range and the separation from the main episode are the two defining characteristics of pre- and post-episodes.

Since the lightning discharges are stochastic and can occur at any time, the frequency-sweeping receiver can dwell at any fre- quency during the time of the discharge. As a consequence, in the general case of straight-line propagation from the source to Cassini, SEDs should be equally distributed at frequencies above the ionospheric cutoff frequency. Since this is not the case for pre- and post-episodes, it is likely that they arise from an iono- spheric propagation effect of SEDs from the main storm cloud, and not from another storm cloud which is within the visible horizon of the spacecraft.

For both panels of Fig.10one can see that the temporal dif- ference between the center of the respective main episode and the pre- or post-episode is around four hours. This translates to a western longitude difference of ∼120^◦, which means that they are observed at a time when the storm cloud is beyond the visible horizon. Hence, we suggest that the existence of pre- and post-episodes is a consequence of the over-the-horizon effect, which will be described in more detail in Sect.5.3. It has already been observed for previous SED storms that the over- the-horizon effect is also frequency dependent, and frequencies above 10 MHz are almost never observed beyond the visible

0 3 6 9 12 15 18 21 24

−80

−60

−40

−20 0 20 40 60 80

Local time [hour]

Kronocentric latitude [°]

Cassini pre−episodes post−episodes

Fig. 11. Local time and kronocentric latitude ofCassini during the recording of pre-episodes (magenta stars) and post-episodes (cyan stars). The black dots show the position ofCassiniin local time and latitude from 27 November 2007 until 15 July 2008 with a resolution of one dot per hour.

horizon (Zarka et al. 2006; Fischer et al. 2007b; Gautier et al. 2013). The pre- and post-episodes show an even more restricted frequency range, and they are a new phenomenon which occurred first with SED storm F. There are a few cases of SED episodes with three parts, that is a main episode which is accompanied by a pre-episode and a post-episode, but usually there is either a pre-episode or a post-episode. Figure 9shows that the absolute majority of all 49 pre-episodes and 34 post- episodes are shorter than one hour, and almost all of them are shorter than 2.5 h. The mean duration of the 83 pre- and post- episodes is 0.97 h. According to our definition, a short pre- or post-episode is not regarded as a full episode, since only together with its main episode it represents the SED activity of one Sat- urn rotation viewed from the spacecraft. Nevertheless, we show the statistics of the pre- and post-episodes in Fig.9 since they are a new and interesting phenomenon. The duration of the main episodes of Fig.9is determined without taking the durations of the pre- or post-episodes into account.

Figure11shows the position ofCassiniin local time and kro- nocentric latitude during the times when pre-episodes (magenta stars) or post-episodes (cyan stars) were recorded. It can be clearly seen that pre- and post-episodes were preferentially observed from±3 h around local noon, that is when the storm cloud was either located around local dawn or local dusk. Both pre- and post-episodes also rather tended to occur whenCassini was at northern latitudes. The black dots show which regions of local time and latitude were sampled byCassiniduring SED storm F.Cassiniwas mostly on the morning side in the southern hemisphere and on the afternoon side in the northern hemi- sphere. The equatorial plane was crossed at almost fixed local times, around 23 LT at periapsis and around 11 LT at apoapsis.

TheCassinilatitude was increasing with time, see also Fig.1.

5.2. Distribution of episodes in subspacecraft western longitude

The course of SED storm F can be illustrated with the following Figs.12and13which plot the subspacecraft western longitude ranges of SED episodes as a function of time. Due to the long duration of SED storm F, we have subdivided the plot of SED

western longitude ranges versus time into two figures. Figure12 extends from the beginning of the storm in the end of November 2007 until mid-March 2008, and Fig.13 shows the longitudi- nal range in the same format from mid-March to the end of the storm in mid-July 2008. The western longitude ranges of the SED episodes are displayed as almost vertical black lines in dif- ferent line styles (solid, dashed, dotted) depending on the number of SEDs of the respective episode (≥200, 20–200, <20). Each line is drawn from the time/western longitude coordinate when the SED episode starts until it ends, with the end point always at a larger western longitude than the start point (i.e., we add 360^◦for end points with western longitudes smaller than at start points). This leads to a clearer arrangement compared to a plot with a strict western longitude range from 0^◦to only 360^◦, and it can be seen in Figs.12and13that ay-axis range over 1.5 rota- tions (0^◦−540^◦) is sufficient to display all SED storm F episodes in such a way.

For each SED episode there is a red asterisk which is located roughly in the middle of each episode. It marks the mean western longitude at the so-called episode center time, which is the mean time of all SEDs from the respective episode. Similarly, the mean western longitude is the mean longitude of all SEDs from one episode. In Fig.12these red asterisks gather around the almost horizontal solid red line, which displays the west longitude of the visible storm cloudF¹ as a function of time. The solid red line has a slope of∼0.35^◦per day as stated in Eq. (1). A linear fit of the center times of all SED episodes with more than 20 SEDs versus western longitude over the time of Fig.12(start of storm until 15 March 2008; and excluding episodes with a mean west- ern longitude smaller than 200^◦and larger than 360^◦) gives a line with a slope of (0.12±0.12)^◦per day, which means it is some- what smaller than the drift of the visible storm cloud. However, another linear fit of the same parameters over the time of Fig.13 (15 March 2008 until end of storm) gives a line with a slope of (0.36±0.10)^◦/day with the intercept (115±48)^◦. In this case the slope of the fitted line is close to the∼0.35^◦per day for the vis- ible storm cellF¹. The second storm cellF² has practically the same slope as storm cellF¹, but its intercept of 124^◦(see Eq. (2)) is 31^◦smaller than the intercept ofF¹. The intercept ofF²is rel- atively close to the intercept of the fitted line, which means that our linear fit is close to the position of storm cellF². This can be seen in Fig.13, where the red asterisks rather gather around the dashed red line describing the western longitude drift of the sec- ond storm cellF²than around the solid red line of storm cellF¹. This is a clear indication that (besides the initial storm cellF¹) the second storm cloudF², which emerged in mid-March 2008, is also a thunderstorm emitting SEDs. Other arguments support- ing this notion is the large optical brightness of the storm cellF² as it can be seen in the right panel of Fig.6, and the increased longitude range of SED episodes in the second half of the storm.

The average longitude range of all SED episodes (pre- and post- episodes excluded) of Fig.12from the beginning of the storm until mid-March 2008 is 165^◦, and the average longitude range of all SED episodes of Fig.13 from mid-March 2008 until the end of the storm is 188^◦. The difference of 23^◦ is close to the longitudinal separation of the visible storm cloudsF¹andF²of 27^◦, suggesting that both storm clouds emit SEDs in the second half of SED storm F.

The western longitude of the third visible cloudS³ is indi- cated in Figs.12 and13by a barely visible red dotted line that starts in the end of January 2008 in Fig. 12and ends in early April 2008 in Fig. 13. During the course of the time it drifts to larger western longitudes with a rate of∼0.92^◦per day (see Eq. (3)). In the days after mid-March it has drifted to a western